PreCM: The Padding-based Rotation Equivariant Convolution Mode for Semantic Segmentation

Semantic segmentation is an important branch of image processing and computer vision. With the popularity of deep learning, various deep semantic segmentation networks have been proposed for pixel-level classification and segmentation tasks. However, the imaging angles are often arbitrary in real world, such as water body images in remote sensing, and capillary and polyp images in medical field, and we usually cannot obtain prior orientation information to guide these networks to extract more effective features. Additionally, learning the features of objects with multiple orientation information is also challenging, as most CNN-based semantic segmentation networks do not have rotation equivariance to resist the disturbance from orientation information. To address the same, in this paper, we first establish a universal convolution-group framework to more fully utilize the orientation information and make the networks rotation equivariant. Then, we mathematically construct the padding-based rotation equivariant convolution mode (PreCM), which can be used not only for multi-scale images and convolution kernels, but also as a replacement component to replace multiple convolutions, like dilated convolution, transposed convolution, variable stride convolution, etc. In order to verify the realization of rotation equivariance, a new evaluation metric named rotation difference (RD) is finally proposed. The experiments carried out on the datesets Satellite Images of Water Bodies, DRIVE and Floodnet show that the PreCM-based networks can achieve better segmentation performance than the original and data augmentation-based networks. In terms of the average RD value, the former is 0% and the latter two are respectively 7.0503% and 3.2606%. Last but not least, PreCM also effectively enhances the robustness of networks to rotation perturbations.